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| Author | : Sergio Albeverio |
| Publisher | : Cambridge University Press |
| Total Pages | : 528 |
| Release | : 1992-06-26 |
| Genre | : Mathematics |
| ISBN | : 9780521419291 |
A collection of essays by many of the closest co-workers of Raphael Høegh-Krohn.
| Author | : Sergio Albeverio |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 348 |
| Release | : 2000 |
| Genre | : Mathematics |
| ISBN | : 9780821819593 |
This volume and "IStochastic Processes, Physics and Geometry: New Interplays II" present state-of-the-art research currently unfolding at the interface between mathematics and physics. Included are select articles from the international conference held in Leipzig (Germany) in honor of Sergio Albeverio's sixtieth birthday. The theme of the conference, "Infinite Dimensional (Stochastic) Analysis and Quantum Physics", was chosen to reflect Albeverio's wide-ranging scientific interests. The articles in these books reflect that broad range of interests and provide a detailed overview highlighting the deep interplay among stochastic processes, mathematical physics, and geometry. The contributions are written by internationally recognized experts in the fields of stochastic analysis, linear and nonlinear (deterministic and stochastic) PDEs, infinite dimensional analysis, functional analysis, commutative and noncommutative probability theory, integrable systems, quantum and statistical mechanics, geometric quantization, and neural networks. Also included are applications in biology and other areas. Most of the contributions are high-level research papers. However, there are also some overviews on topics of general interest. The articles selected for publication in these volumes were specifically chosen to introduce readers to advanced topics, to emphasize interdisciplinary connections, and to stress future research directions. Volume I contains contributions from invited speakers; Volume II contains additional contributed papers. Members of the Canadian Mathematical Society may order at the AMS member price.
| Author | : Michael Craig Cranston |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 634 |
| Release | : 1995 |
| Genre | : Mathematics |
| ISBN | : 0821802895 |
This book deals with current developments in stochastic analysis and its interfaces with partial differential equations, dynamical systems, mathematical physics, differential geometry, and infinite-dimensional analysis. The origins of stochastic analysis can be found in Norbert Wiener's construction of Brownian motion and Kiyosi Itô's subsequent development of stochastic integration and the closely related theory of stochastic (ordinary) differential equations. The papers in this volume indicate the great strides that have been made in recent years, exhibiting the tremendous power and diversity of stochastic analysis while giving a clear indication of the unsolved problems and possible future directions for development. The collection represents the proceedings of the AMS Summer Institute on Stochastic Analysis, held in July 1993 at Cornell University. Many of the papers are largely expository in character while containing new results.
| Author | : J.E. Lindstrom |
| Publisher | : CRC Press |
| Total Pages | : 302 |
| Release | : 1993-12-08 |
| Genre | : Mathematics |
| ISBN | : 9782881249488 |
First published in 1993. Routledge is an imprint of Taylor & Francis, an informa company.
| Author | : Ana Isabel Cardoso |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 455 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401102198 |
Proceedings of the NATO Advanced Study Institute, Funchal, Madeira, Portugal, August 6--19, 1993
| Author | : Fritz Gesztesy |
| Publisher | : American Mathematical Society |
| Total Pages | : 946 |
| Release | : 2024-09-24 |
| Genre | : Mathematics |
| ISBN | : 1470476665 |
This book provides a detailed treatment of the various facets of modern Sturm?Liouville theory, including such topics as Weyl?Titchmarsh theory, classical, renormalized, and perturbative oscillation theory, boundary data maps, traces and determinants for Sturm?Liouville operators, strongly singular Sturm?Liouville differential operators, generalized boundary values, and Sturm?Liouville operators with distributional coefficients. To illustrate the theory, the book develops an array of examples from Floquet theory to short-range scattering theory, higher-order KdV trace relations, elliptic and algebro-geometric finite gap potentials, reflectionless potentials and the Sodin?Yuditskii class, as well as a detailed collection of singular examples, such as the Bessel, generalized Bessel, and Jacobi operators. A set of appendices contains background on the basics of linear operators and spectral theory in Hilbert spaces, Schatten?von Neumann classes of compact operators, self-adjoint extensions of symmetric operators, including the Friedrichs and Krein?von Neumann extensions, boundary triplets for ODEs, Krein-type resolvent formulas, sesquilinear forms, Nevanlinna?Herglotz functions, and Bessel functions.
| Author | : Sergio Albeverio |
| Publisher | : Cambridge University Press |
| Total Pages | : 454 |
| Release | : 2000-03-13 |
| Genre | : Mathematics |
| ISBN | : 9780521779128 |
This is a systematic mathematical study of differential (and more general self-adjoint) operators.
| Author | : Niels Jacob |
| Publisher | : World Scientific |
| Total Pages | : 504 |
| Release | : 2005-06-14 |
| Genre | : Mathematics |
| ISBN | : 1783260246 |
This volume concentrates on how to construct a Markov process by starting with a suitable pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub-Markovian semigroups and processes constructed by using the Martingale problem are at the center of the considerations. The potential theory of these processes is further developed and applications are discussed. Due to the non-locality of the generators, the processes are jump processes and their relations to Levy processes are investigated. Special emphasis is given to the symbol of a process, a notion which generalizes that of the characteristic exponent of a Levy process and provides a natural link to pseudo-differential operator theory./a
| Author | : Michel Laurent Lapidus |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 534 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0821836374 |
This volume offers an excellent selection of cutting-edge articles about fractal geometry, covering the great breadth of mathematics and related areas touched by this subject. Included are rich survey articles and fine expository papers. The high-quality contributions to the volume by well-known researchers--including two articles by Mandelbrot--provide a solid cross-section of recent research representing the richness and variety of contemporary advances in and around fractal geometry. In demonstrating the vitality and diversity of the field, this book will motivate further investigation into the many open problems and inspire future research directions. It is suitable for graduate students and researchers interested in fractal geometry and its applications. This is a two-part volume. Part 1 covers analysis, number theory, and dynamical systems; Part 2, multifractals, probability and statistical mechanics, and applications.
| Author | : Jun Kigami |
| Publisher | : Cambridge University Press |
| Total Pages | : 238 |
| Release | : 2001-06-07 |
| Genre | : Mathematics |
| ISBN | : 0521793211 |
This book covers analysis on fractals, a developing area of mathematics which focuses on the dynamical aspects of fractals, such as heat diffusion on fractals and the vibration of a material with fractal structure. The book provides a self-contained introduction to the subject, starting from the basic geometry of self-similar sets and going on to discuss recent results, including the properties of eigenvalues and eigenfunctions of the Laplacians, and the asymptotical behaviors of heat kernels on self-similar sets. Requiring only a basic knowledge of advanced analysis, general topology and measure theory, this book will be of value to graduate students and researchers in analysis and probability theory. It will also be useful as a supplementary text for graduate courses covering fractals.
